Question

How do you solve `8n ^ { 2} + 56n = - 48`?

Answer 1

`8n^2+56n= -48`
`8n^2+56n+48=0`

Divide by 8 throughout `\implies`

`n^2+7n+6 = 0`

Now you factorize 6 and look for the combination that results in +6 and has a sum of +7.

We have the following pairs of roots`(1,6),(-1,-6),(3,2),(-3,-2)` that give +6. The first set gives the sum of +7. So the equation can be written as

`n^2+n+6n+6 = 0`
`n(n+1)+6(n+1) = 0`
`(n+1)(n+6) = 0`
`n = -1,-6`